Question

In the following figure, AB || DC, AB = 6 cm, AE = 3 cm, CE = 4 cm, ED = 8 cm, determine BE and CD.

Answer 1

So, triangles ΔAEB and ΔCED are similar (vertically opposite angles and corresponding angles are equal).

△AEB ∼ △CED (AA similarity)

Thus, corresponding sides are proportional:

`(AE)/(CE) = (BE)/(ED) = (AB)/(CD)`

Substitute the given values:

`3/4 = (BE)/8 = 6/(CD)`

⇒ Let’s find BE:

`3/4 = (BE)/8`

`BE = 3/4 xx 8`

∴ BE = 6 cm

⇒ Let’s find CD:

`3/4 = 6/(CD)`

`CD = (6 xx 4)/3`

∴ CD = 8 cm

Hence, BE = 6 cm and CD = 8 cm.